I've already contacted my web host to ask them to look into it, but server load spikes are notoriously difficult to diagnose unless we can catch it happening or discern a pattern. So at this point it would help if people could post the times (say in EST) when these spikes occur, so we can see if there's a pattern, like if they occur at regular intervals or at the same times of day. That should help the web host track down the issue.
[Mod: No need to report time now, it's automated: Dear Steve, (Forum getting busy signal)]